Todaymanyeconomists, engineers and mathematicians are familiar with
linear programming and are able to apply it. This is owing to the
following facts: during the last 25 years efficient methods have been
developed; at the same time sufficient computer capacity became
available; finally, in many different fields, linear programs have
turned out to be appropriate models for solving practical problems.
However, to apply the theory and the methods of linear programming, it
is required that the data determining a linear program be fixed known
numbers. This condition is not fulfilled in many practical situations,
e. g. when the data are demands, technological coefficients, available
capacities, cost rates and so on. It may happen that such data are
random variables. In this case, it seems to be common practice to
replace these random variables by their mean values and solve the
resulting linear program. By 1960 various authors had already recog-
nized that this approach is unsound: between 1955 and 1960 there were
such papers as "Linear Programming under Uncertainty", "Stochastic
Linear Pro- gramming with Applications to Agricultural Economics",
"Chance Constrained Programming", "Inequalities for Stochastic Linear
Programming Problems" and "An Approach to Linear Programming under
Uncertainty".